The number 1248
1248 is a composite number with 24 divisors. Its prime factorisation is × 3 × 13. Divisors (24): 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 32, 39, 48, 52, 78 … 1248.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
1248 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
1248 is composite. Its prime factorisation is
- 3
The divisors add up to 3528; without 1248 itself that is 2280, so 1248 is abundant (2280 is more than 1248). Euler's totient φ(1248) = 384 numbers up to 1248 share no factor with it.
- 4
The digits of 1248 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 39 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1248 = 2^{5} \times 3 \times 13 \]1248 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 3528 |
| Euler totient φ(n) | 384 |
| Square | 1557504 |
| Cube | 1943764992 |
| Square root | 35.327043 (= 4√78) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 39 |
| Scientific notation | 1.248 × |
1248 in other forms
| Form | Value |
|---|---|
| In words | one thousand two hundred and forty-eight |
| Roman numerals | MCCXLVIII |
| Binary (base 2) | 10011100000 |
| Octal (base 8) | 2340 |
| Hexadecimal (base 16) | 4E0 |
| Base 3 | 1201020 |
| As time | 1248 seconds = 20 min 48 s |
Is 1248 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1248 ÷ 2 = 624) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1248 ÷ 3 = 416) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1248 ÷ 4 = 312) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (1248 ÷ 6 = 208) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | A number is divisible by 7 if double the last digit and subtract it from the rest: the result is a multiple of 7. |
| 8 | Yes (1248 ÷ 8 = 156) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (1248 ÷ 12 = 104) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1248 a prime number?
No. 1248 = × 3 × 13, so it is divisible by 2.
What are the factors of 1248?
1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 32, 39, 48, 52, 78, 96, 104, 156, 208, 312, 416, 624, 1248.
What is 1248 in binary?
10011100000 (hexadecimal 4E0, octal 2340).
What is the square root of 1248?
About 35.3270, exactly 4√78.
What is 1248 in Roman numerals?
MCCXLVIII.
Is 1248 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 1248?
It is a composite number with 24 divisors.